The basic principles and techniques for electromagnetic logging for earth formations are well known. Induction logging to determine the resistivity (or its inverse, conductivity) of earth formations adjacent a borehole, for example, has long been a standard and important technique in the search for and recovery of subterranean petroleum deposits. In brief, the measurements are made by inducing electrical current flows in nearby formations in response to an AC transmitter signal, and then measuring the appropriate characteristics of a receiver signal generated by the induced current flows. The formation properties identified by these signals are then recorded in a log at the surface as a function of the depth of the tool in the borehole.
It is well known that subterranean formations surrounding an earth borehole may be anisotropic with regard to the conduction of electrical currents. The phenomenon of electrical anisotropy is generally a consequence of either microscopic or macroscopic geometry, or a combination thereof, as follows.
In many sedimentary strata, electrical current flows more easily in a direction parallel to the bedding planes, as opposed to a direction perpendicular to the bedding planes. One reason is that a great number of mineral crystals possess a flat or elongated shape (e.g., mica or kaolin). At the time they were laid down, they naturally took on an orientation parallel to the plane of sedimentation. The interstices in the formations are, therefore, generally parallel to the bedding plane, and the current is able to easily travel along these interstices which often contain electrically conductive mineralized water. Such electrical anisotropy, sometimes called microscopic anisotropy, is observed mostly in shales.
Macroscopic anisotropy, on the other hand, occurs in subterranean formations made up of a series of relatively thin beds having different lithological characteristics and, therefore different resistivities. In well logging systems, the distances between the electrodes or antennas are great enough that the volume involved in a measurement may include several such thin beds. When individual layers are neither delineated nor resolved by a logging tool, the tool responds to the formation as if it were a macroscopically anisotropic formation. A thinly laminated sand/shale sequence is a particularly important example of a macroscopically anisotropic formation.
If a sample is cut from a subterranean formation, the resistivity of the sample measured with current flowing parallel to the bedding planes is called the transverse or horizontal resistivity ρH. The inverse of ρH is the horizontal conductivity σH. The resistivity of the sample measured with a current flowing perpendicular to the bedding plane is called the longitudinal or vertical resistivity, ρv, and its inverse the vertical conductivity σv. The anisotropy coefficient λ is defined as:
                    λ        =                                                            σ                h                            /                              σ                v                                              .                                    (        1        )            
In situations where the borehole intersects the formation substantially perpendicular to the bedding planes, conventional induction and propagation well logging tools are sensitive almost exclusively to the horizontal component of the formation resistivity. This is a consequence of the induced currents flowing in horizontal planes in the absence of formation dip or well deviation. Indeed, in the context of galvanic devices, the lack of sensitivity to anisotropy is even more stringent due to the “paradox of anisotropy,” which states that any array of electrodes or sensors deployed along the axis of a wellbore in a vertical well is insensitive to the vertical component of resistivity, despite the intuitive expectation to the contrary.
At present, there exists only one commercial instrument that measures the vertical resistivity. B. Kriegshauser, et al., describe this instrument in “A new multicomponent induction logging tool to resolve anisotropic formations,” 41st Annual Logging Symposium, Society of Professional Well Log Analysts, paper D, pps. 1–14, 2000. This instrument employs multiple multi-component coils (i.e., transmitter and receiver coils having axial and transverse orientations). This instrument may be unduly complex and provide measurements that are difficult to interpret. Further, the design of this wireline instrument may not be adaptable to a measurement while drilling (MWD) implementation. A simpler method and apparatus for measuring vertical resistivity would be desirable.